B.1Lemma B.1 (Lemma 15.12 in [1]}) 

Consider direction \(u\)  with directional coordinates \(a=(a_1, a_2, a_3, a_4)\) . Then
\(D_{u}B_{ijkl}^d(v)=& d\left\lbrace a_1 B_{i-1,j,k,l}^{d-1}(v) + a_2 B_{i,j-1,k,l}^{d-1}(v) \right. \nonumber \\& ~~~~~~~~~~~~~~~~~~~~~\left. + a_3 B_{i,j,k-1,l}^{d-1}(v) + a_4 B_{i,j,k,l-1}^{d-1}(v)\right\rbrace ,\) 
